Small-signal Dynamic Model Research Articles

Small Signal Stability Investigation of the MMC-HVDC Grid

This paper presents a small-signal dynamic model for a modular multilevel converter (MMC) based HVDC grid, and then systematically i) identifies the system dominant oscillatory modes, ii) quantifies their propensity to instability phenomena, and iii) devises appropriate countermeasures. Based on the developed model, the eigen structure of an HVDC grid is characterized and the impact of the system parameters, configuration, AC system strength and operating point on the damping ratios of the oscillatory modes, and consequently the HVDC grid stability, are investigated. The model is also applied to systematically determine the sensitive parameters and optimize them to mitigate oscillatory modes and prevent instability. The eigen analysis results are verified based on time-domain simulation studies in the PSCAD/EMTDC platform.

Cooperative Control to Suppress Unbalanced and Harmonic Distortion in the Distribution Network With Inverter-Based Distributed Generators

In the contemporary distribution network, unbalanced and harmonic distortions have been considered some major power quality problems, which have escalated especially due to the high penetration of unbalanced and nonlinear loads. This study first analyzes the dispute around the distortion restraint and grid-connected unbalanced/harmonic current suppression quantitatively and proposes a distributed control strategy that facilitates an effective suppression of output voltage and grid-connected current, with accurate unbalanced/harmonic power sharing. Compared with the majority of existing studies only addressing the voltage-controlled mode (VCM) inverters, our scheme can also be applied to current-controlled mode (CCM) inverters without adding additional current regulation loops. The proposed control strategy is independent of line parameters and robust to load changes. The corresponding small-signal dynamic model is constructed to analyze the system stability and the controller hardware-in-the-loop simulations aid in determining the outcome of the proposed strategy.

An Accurate Small Signal Dynamic Model for LCC-HVDC

This paper develops an accurate small signal model for line commutated converter based HVDC (LCC-HVDC). The overall process of the model establishment is demonstrated from five parts: AC system, DC system, control system, phase-locked loop (PLL) and the converter. Considering the limitations of the traditional converter equations, the proposed small signal model takes the commutation process into account so that the overlap angle and AC current are calculated with the actual value rather than the estimated value. The accuracy of the proposed model is verified both in the time-domain simulation in PSCAD/EMTDC and by eigenvalue analysis. The results show better performance than the traditional modeling methods, which provides valuable guidance for future LCC-HVDC project design.

Distributed MPC-Based Secondary Control for Energy Storage Systems in a DC Microgrid

In this paper, a novel distributed model predictive control (DMPC) strategy based on voltage observer for multiple energy storage systems (ESs) is firstly proposed to achieve a tradeoff between voltage regulation and power sharing. In order to reduce the impact of communication delay on voltage observer, an improved DMPC consensus algorithm is proposed. This scheme improves the robustness of the system to the delay. Besides, a small-signal dynamic model of a DC microgrid with the improved DMPC controllers is established to analyze its dynamic performance. The time-domain simulation results are presented to verify that, under the constraints of the DC bus voltage, a flexible trade-off between voltage regulation and power distribution can be achieved. Besides, the communication delay problems can be reduced.

A Feedforward Decoupling Control Method for Multi-ports DC Transformer

DC Transformer (DCT) is a new type of intelligent power electronic device using power semiconductors and high-frequency transformer to realize power conversion. Multi-ports DCT has broad applications in DC distribution networks. In this paper, the power transmission characteristics of the phase-shift controlled multi-ports DCT are analyzed. The non-linear coupling characteristics of the output power at different ports are also studied. The small-signal dynamic coupling model of the multi-ports DCT is established. On this basis, a feed-forward term is introduced and constructed in the closed-loop voltage control system. The theoretical analysis shows that the feedforward term can decouple the output voltage of different ports of the multi-ports DCT. The correctness of the feed-forward control method is verified by simulations.

Impact of PLL dynamics on the small-signal stability of the MMC using dynamic phasor modeling in the ABC frame

This paper presents a small-signal dynamic phasor model of the modular multilevel converter including phase-locked loop (PLL) dynamics. A simple PLL model including a low-pass filter at its input and accounting for the harmonic content of the voltage at the point of common coupling is developed to assess the impact of the PLL on small-signal stability. Nonlinear models of the converter, its controllers and the PLL are separately developed and linearized. The linearized models are combined using the component connection method to obtain the overall system matrices. The developed model is verified against a nonlinear averaged model in MATLAB/Simulink, and dynamic phasor models including different harmonic content are compared in terms of their accuracy. Eigenvalue analysis is carried out to study the impact of the PLL and its filter cutoff frequency on the small-signal stability of the converter.

An improved control strategy of virtual synchronous generator under symmetrical grid voltage sag

The virtual synchronous generator (VSG) which mimics the synchronous generator enables the operation of inverter-interfaced distributed generations (DGs) more effectively. However, the insufficiency in the low-voltage ride-through (LVRT) capability of conventional VSG limits its extensive application during the voltage sag condition. In this paper, firstly the performance of conventional VSG under the condition of symmetrical voltage sag is elaborated, and then based on the reference dynamic compensation an improved VSG control strategy is proposed, where the new voltage reference generation algorithm is designated to accommodate to different degrees of voltage sag, avoiding controller switching. Then, a fault current limitation scheme is introduced to guarantee the transient peak current of VSG within an acceptable range, especially during serious system disturbances. When the grid voltage restores to normal, an additional phase angle control loop is implemented to facilitate the smooth and rapid transfer of VSG strategy while the voltage reference is switched back to the rated value. Furthermore, the details of design for the VSG algorithm and the phase angle controller are provided through the formulation of small-signal dynamic model, improving the overall system performance during grid voltage sag. Finally, the validity and effectiveness of the proposed strategy are verified by the hardware-in-the-loop (HIL) simulation results.

Distributed Secondary Voltage Control in Islanded Microgrids With Consideration of Communication Network and Time Delays

The extensive usage of open communication mechanisms in distributed secondary control of islanded microgrids (MGs) suggests that the effects of the communication network and time delays on system performance cannot be negligible. Based on the relationship between convergence and algebraic connectivity, this paper proposes an optimal design for a directed communication topology and pinning location through the mirror operation and global propagation rates, respectively. Alternatively, a small-signal dynamic model of an MG equipped with time-delayed distributed secondary voltage control is derived, to investigate the delay-dependent stability of MG system in terms of the controller, network and pinning conditions. An analytical formula is then developed to determine the individual delay margins with respect to different sets of controller gains and pinning. Through a series of trials, the qualitative effects of controller parameters and pinning conditions on delay margins can be used to guide the design of both controllers and pinning for the improved system performance. The effectiveness of proposed methodology is verified via the real-time hardware-in-the-loop (HIL) simulations.

Transient Analysis of Microgrids With Parallel Synchronous Generators and Virtual Synchronous Generators

In recent years, the increasing penetration of distributed generation in microgrids challenges the control and coordination of energy resources. Especially in microgrids with virtual synchronous generator (VSG)-controlled converters and conventional synchronous generators (SG), the inherent inertia difference (i.e., the VSG and SG) results in a poor transient performance when the VSG and/or loads are cut in/out. Thus, this paper explores the transient performance of microgrids with parallel VSG and SG systems. More importantly, a novel pre-synchronization control method is proposed to eliminate the phase jump while meeting the requirements in case of closures or re-closures of generation units. A small-signal dynamic model is presented, and accordingly, the VSG inertia and its damping can be designed considering the capacity ratio of VSG and SG units. In addition, with the power angle stability analysis, an active power provision strategy is introduced to suppress the transient power oscillation due to the inertia difference. Finally, the feasibility of the proposed methods is verified by simulations on a microgrid consisting of parallel VSG and SG units.

Stability enhancement strategy of virtual synchronous generator for cascaded multilevel converter based energy storage system under weak grid conditions

Considering that the low-voltage and small capacity ratings of the traditional distributed energy storage system (ESS) cannot meet the increasing capacity of distributed generations, this study describes a cascaded multilevel converter-based ESS. In addition, the virtual synchronous generator (VSG) as a promising solution to enhance the system's inertia is studied. However, some studies indicate that VSG suffers from the inherent resonance near synchronous frequency under weak grid conditions, which may result in power oscillation and even deteriorate the system stability. In this work, the resonance mechanism is investigated with an established wide-band small-signal dynamic model. It is revealed that the resonance poles caused by the small impedance ratio on the AC side introduce a phase lag jump of 180°, which decreases the phase margin of VSG, leading to synchronous power oscillation (SPO). The influence of control parameters on the power oscillation is investigated with the eigenvalue analysis method. Accordingly, a differential feedforward compensation-based SPO suppression strategy is proposed. The stability margins are significantly enhanced with this method. The validity of the SPO analysis and suppression method is verified with simulation and a 10 kW experimental prototype.

Small-Signal Stability Analysis of Photovoltaic-Hydro Integrated Systems on Ultra-Low Frequency Oscillation

In recent years, ultralow-frequency oscillation has repeatedly occurred in asynchronously connected regional power systems and brought serious threats to the operation of power grids. This phenomenon is mainly caused by hydropower units because of the water hammer effect of turbines and the inappropriate Proportional-Integral-Derivative (PID) parameters of governors. In practice, hydropower and solar power are often combined to form an integrated photovoltaic (PV)-hydro system to realize complementary renewable power generation. This paper studies ultralow-frequency oscillations in integrated PV-hydro systems and analyzes the impacts of PV generation on ultralow-frequency oscillation modes. Firstly, the negative damping problem of hydro turbines and governors in the ultralow-frequency band was analyzed through the damping torque analysis. Subsequently, in order to analyze the impact of PV generation, a small-signal dynamic model of the integrated PV-hydro system was established, considering a detailed dynamic model of PV generation. Based on the small-signal dynamic model, a two-zone and four-machine system and an actual integrated PV-hydro system were selected to analyze the influence of PV generation on ultralow-frequency oscillation modes under different scenarios of PV output powers and locations. The analysis results showed that PV dynamics do not participate in ultralow-frequency oscillation modes and the changes of PV generation to power flows do not cause obvious changes in ultralow-frequency oscillation mode. Ultra-low frequency oscillations are mainly affected by sources participating in the frequency adjustment of systems.

Pinning-Based Hierarchical and Distributed Cooperative Control for AC Microgrid Clusters

With the large-scale application of microgrids (MGs), interconnecting nearby MGs to form an MG cluster (MGC) enables a higher utilization of renewable sources. This article presents a pinning-based hierarchical and distributed cooperative control strategy for AC MGC, which includes distributed generation (DG)-layer, MG-layer, and MGC-layer controls. The DG-layer control regulates the local voltage/current of each DG unit. The MG-layer control is performed for each individual MG, managing DG units in a cooperative manner through several sparse communication networks. By representing each MG as an MG agent, the MGC-layer control coordinates MGs based on a higher level peer-to-peer communication network among MG agents. The interaction between MG-layer and MGC-layer is established by pinning some DG units of each MG to communicate with the MG agent. Compared with the existing literature, the contributions of this article are: 1) simultaneously realizing multiple control objectives in the MGC system level including frequency/voltage regulation and active/reactive power sharing; 2) presenting a systematic approach to construct a unified small-signal dynamic model of the MGC system; and 3) performing a detailed small-signal stability analysis to evaluate the system dynamic performance. Time-domain simulation and experiments are carried out to validate the effectiveness of the proposed methods.

Distributed Control of VSC-MTDC Systems Considering Tradeoff Between Voltage Regulation and Power Sharing

This paper presents a novel distributed voltage control method for multi-terminal direct current (MTDC) systems based on the average consensus algorithm. The proposed method combines the idea of secondary integral voltage control and regulator synchronization problem. It realizes adjustable tradeoff between two conflicting control objectives, that is, voltage regulation and power sharing. The proposed control algorithm only needs a low-bandwidth communication between two adjacent voltage source converters (VSCs) and local information to work effectively. Moreover, regarding the system dynamic response, a parameter tuning method for the proposed controller is provided to achieve the fastest convergence of the distributed control algorithm. This paper also develops a small-signal dynamic model for VSC-MTDC systems with distributed controllers to evaluate the system dynamic performance. The proposed method is validated by time-domain simulation of a 4-terminal VSC-MTDC system. The simulation results show that flexible tradeoff between voltage regulation and power sharing can be achieved under necessary constraints on the DC bus voltages and power sharing ratio.

Research on Control Strategy of Quasi-Z Source Network DC/DC Converter for Fuel Cell Vehicle

DC/DC converter for fuel cell vehicles is required to operate in high voltage gain and wide voltage range conditions, which traditional boost converter is difficult to meet. In this paper, the control strategy of a quasi-zsource boost converter used in fuel cell vehicles is studied. Based on the small signal dynamic modeling method, the double-closed-loop control strategy of voltage and current is adopted. In addition, the input voltage feedforward compensation control strategy is adopted to improve performance in rejecting Input voltage disturbance. A 400W prototype is built for experimental verification. Experimental results show that the proposed input voltage feedforward compensation strategy and double- closed-loop control strategy of voltage and current effectively improve the system dynamic response speed and robustness.

Improved virtual synchronous generator with transient damping link and its seamless transfer control for cascaded H‐bridge multilevel converter‐based energy storage system

To improve the efficiency, power quality and reliability for large-scale renewable energy sources (RESs), a transformerless energy storage system (ESS) based on cascaded H-bridge converter (CHB) is presented in this study. Furthermore, the virtual synchronous generator (VSG) control is investigated to make ESS integrated to grid friendly. This study points out and discusses that the primary frequency regulation (PFR) of ESS will be deteriorated by the damping link in VSG due to the coupling problem, and to this end, the proposed virtual transient damping link (TDL) is introduced to simulate the transient and steady-state characteristics of synchronous generators (SGs) accurately without affecting the frequency regulation of ESS. In addition, the small-signal dynamic model of VSG with TDL is established, besides, the influence of VSG control parameters on system stability is analysed by the generalised root locus method and the parameters are quantitatively designed. Furthermore, a direct voltage-phase discrimination-based pre-synchronising control strategy is proposed to realise the seamless transfer between islanded and grid-connected modes for ESS. The simulation and 10 kW prototype experimental results verify the effectiveness of the proposed control strategies and the theoretical analysis.

Open‐loop transfer functions of buck–boost converter by circuit‐averaging technique

This study shows the derivation of the power-stage transfer functions and input and output impedances of a buck–boost pulse width-modulated (PWM) dc–dc converter operating in continuous-conduction mode. The expressions are derived using the small-signal model obtained by the circuit-averaging technique. Using the small-signal dynamic model, both transient and frequency domain characteristics are determined. An example buck–boost converter with the following specifications was considered: supply voltage 12 V, output voltage 5 V, switching frequency 200 kHz, and output power 10 W. The modification of the power-stage transfer function to include the time delay between the MOSFET gate drive and the duty cycle is considered and is modelled by the first-order Padè approximation. The theoretical predictions were verified by experiments and excellent agreement between the results was observed.

Research on Composite Control Strategy of Quasi-Z-Source DC–DC Converter for Fuel Cell Vehicles

The DC–DC converter for fuel cell vehicles requires high gain and wide voltage input range to boost the voltage of the fuel cell. However, with the traditional boost converter, it is difficult to meet the requirements of the fuel cell vehicle power system. Based on a quasi-Z-source network DC–DC converter, this paper proposes a composite controller, which includes a feedforward compensation network and feedback control to meet the control robustness requirement of the fuel cell vehicle power system. The dynamic model of the converter is obtained by using the state space averaging method and the small-signal dynamic modeling method. The input voltage and load disturbance experiments are performed on the DC–DC converter. Moreover, the converter is tested under the worldwide harmonised light vehicle test procedure (WLTP) to validate the effectiveness of the proposed composite controller. The simulation and experiment results show that the proposed composite controller effectively enhances the converter’s ability to resist input and load disturbance, and improves the dynamic response performance of the DC–DC converter for fuel cell vehicles.

A Two-Layer Distributed Cooperative Control Method for Islanded Networked Microgrid Systems

This paper presents a two-layer distributed cooperative control method for networked microgrid (NMG) systems, taking into account the proprietary nature of microgrid (MG) owners. The proposed control architecture consists of an MG-control layer and an NMG-control layer. In the MG layer, the primary and distributed secondary controls realize accurate power sharing among distributed generators (DGs) and the frequency/voltage reference following within each MG. In the NMG layer, the tertiary control enables regulation of the power flowing through the point of common coupling (PCC) of each MG in a decentralized manner. Furthermore, distributed quaternary control restores the system frequency and critical bus voltage to their nominal values and ensures accurate power sharing among MGs. A small-signal dynamic model is developed to evaluate the dynamic performance of NMG systems with the proposed control method. Time-domain simulations and experiments on NMG test systems are performed to validate the effectiveness of the proposed method.

Optimal Design for Distributed Secondary Voltage Control in Islanded Microgrids: Communication Topology and Controller

This paper proposes an optimal design algorithm for distributed secondary voltage control in islanded microgrids (MGs), including communication topology and controller gains. First, upon the consensus-based secondary voltage control, the sufficient condition for network connectivity of communication topology is revealed by the reachability matrix. A multi-objective optimization criterion is first proposed for the network design, taking the convergence performance, network-relevant time delays, and communication costs into consideration. After obtaining the Pareto frontier of this multi-objective model, an optimal network is selected to meet the practical requirements. Based on static output feedback, a small-signal dynamic model of an MG installed with a secondary voltage controller is established, where the distributed secondary voltage controller can be converted into an equivalent decentralized controller. Thereby, a linear quadratic regulator is formulated for the near-optimal design of controller parameters. Our approach customizes the optimal design framework of the topology and controller, which have been largely ignored in the existing literatures. Therefore, it promises to improve the performance of distributed secondary control. The effectiveness of the proposed methodology is verified by a simulation study.

Coordination strategies of distributed energy resources including FESS, DEG, FC and WTG in load frequency control (LFC) scheme of hybrid isolated micro-grid

This paper presents a novel load frequency control (LFC) model for a stand-alone hybrid micro-grid in the presence of renewable energy resources. A perilous fact in operation of isolated micro-grid is to deal with a low-inertia system owing to the unpredictable structure and the intermittent fluctuation of RESs. In comparison to the conventional power system, the rate of change of frequency (RoCoF) is high in isolated micro-gird. Therefore, the need for fast frequency response provision delivered by existing distributed energy resources, which are inverter-connected technologies, arises. Some distributed energy resources (DERs) can be considered as potential reserves for active power injection in the load frequency control scheme. The simulation results depict that renewable energy resources like diesel engine generator (DEG), Fuel Cell (FC), Flywheel Energy Storage System (FESS) and Wind Turbine Generator (WTG) have the capability to improve frequency excursion during various operating conditions if comprehensive small-signal dynamic models for RESs are introduced in isolated micro-grid and proper contribution of them in load frequency control studies is considered.